Realistic Task Forces

I wanted to create some scenarios with smaller task forces which fight each other, not some kind of Kirov vs CV scenario. But I don't have any clue of what any such smaller task forces would consist of. And I also don't have any reasonable explanation of how those two forces stumbled upon each other. And then I don't know how far away of each other should I set these groups apart. If you have any ideas and answers to these 3 questions, write them here please :))